Spatial distributions of droplet size and velocity in air heated spray
Measured by interferometric laser imaging technique
by
Goro Takeuchi (1), Tatsuya Kawaguchi (2), Koichi Hishida (1), Masanobu Maeda (1) and Martin Sommerfeld (3)
(1)
Keio University
Department of System Design Engineering Faculty of Science and Technology
Hiyoshi 3-13-1, Kohoku-ku, Yokohama, Japan
E-Mail: takeuchi@mh.sd.keio.ac.jp
(2)
Tokyo Institute of Technology
Department of Mechanical and Control Engineering
O-okayama 2-12-1, Meguro-ku, Tokyo, Japan
(3)
Visiting professor at Keio University
Martin-Luther-University of Halle
Department of Engineering Science, Institute of Process Engineering
D-06099 Halle (Saale), Germany
ABSTRACT
The behaviour of a water spray centrally injected into a swirling annular jet (initial outer diameter 56.5mm) was studied
experimentally. Two flow conditions were compared, namely a non-heated and a heated airflow issuing into quiescent
air (Figure 1). The water spray was produced using a full cone nozzle mounted centrally into the injection pipe. The
instantaneous spatial distribution of droplet size and velocity was measured applying the interferometric laser imaging
technique (ILIDS). The circular out-of-focus images were first optically squeezed for allowing an easier and more
reliable analysis of the images. The fringe spacing, which is proportional to the droplet diameters, was determined by
discrete Fourier transform and a Gaussian interpolation technique. The droplet velocity was obtained from the
displacement of the squeezed images recorded or two subsequent images. The results demonstrate that the interaction
of the spray with the swirling free jet flow and the established recirculation zone results in bimodal droplet size
distributions for both the non-heated and heated case (Figure 2). As expected, droplet evaporation in the heated case
yields a faster decrease of the mean droplet size along the spray than for the non-heated case.
Fig. 1. Schematics of experimental set-up and
interferometric laser imaging technique
Fig. 2. Size distributions and correlation maps
between diameter and axial velocity at (z,r)=(75,0)
1
1. INTRODUCTION
For understanding the transient spray, not only the averaged size and velocity distributions of droplets are of
importance, but also the instantaneous properties of individual droplets are required to understand the unsteady
behavior of droplets and flow structure, and to evaluate heat and mass transport processes. Interferometric laser
imaging for droplet sizing is a method that provides an instantaneous spatial distribution of droplet size by analyzing
the out-of-focus image of droplets (Glover et al. 1995). The angular phase difference of the external reflection from the
surface and the direct refraction through the droplet allows to derive a relation between fringe spacing and droplet size.
The measurement accuracy depends on the estimation of the size of the out-of-focus image and the fringe spacing.
In the present technique, an advanced imaging technique and accelerated data processing by a fast computer system
was developed whereby the circular images with fringes are optically squeezed into linear images by defocusing
horizontally and focusing vertically (Maeda et al. 2000, 2002, Kawaguchi et al. 2002). The squeezing technique
reduced the involved noise and the signal to noise ratio of the interferogram becomes much better than that of
conventional technique as a consequence. Moreover, the optical compression technique can eliminate distorted or
inclined interference signal resulting from wall reflection and multiple scattering. The preferential fringe acquisition
technique provides genuine interferential signals that give the diameter of particles. The signal processing procedure for
the determination of the droplet diameter requires only one-dimensional information of the fringe spacing which was
evaluated by discrete Fourier transform and Gaussian interpolation technique of the power spectrum. The accurate
diameter determination enables to identify the particles in successive images and to measure the velocity vectors of
each droplet even from images of denser sprays. The direct digital acquisition of images and the fully automated image
processing software provide high quality data for up to six hundred droplets in a frozen image of 10mm x10mm.
Furthermore, the size determination from the scattering pattern of droplets is not affected by the refractive index by the
temperature fluctuation (Kawaguchi et al. 2003). i.e. the diameter coefficient that relates the size of particle and fringe
separation is almost independent of the refractive index.
In this study, the planar droplet sizing technique has been applied for a spray issuing into a heated swirling flow.
Swirling two-phase flows are encountered in a variety of forms in many engineering applications. In combustion
systems the special features of swirling flows are used to establish high mixing rates between the fuel and the swirling
air stream and to enhance flame stability. To improve the understanding of swirling flow, a number of studied have
been carried out in the past. The particle dispersion characteristics in a confined swirling flow were studied by
Sommerfeld et al. (1991, 1993) using a phase-Doppler technique and numerical predictions. Their results demonstrate
the behaviour of different sized particles in a complex flow and the spatial change of the particle-size distribution
throughout the flow field. Hardalupas et al. (1990, 1994) studied the velocity-size correlation of droplets in a liquidfuelled swirl burner. Their results demonstrate the different behavior of different sized droplets in a swirling free jet
emanating from a quarl-type burner nozzle.
2. TEST FACILITY
The test facility for the experimental studies is shown in Figure 3. It consists of an inverter-controlled blower with
variable flow rate, a heater array followed by a pipe system, a swirl generator and a measurement section with quadratic
cross-section (500 × 500mm) and a length of 1000mm. Eight coil-fin-electric-heaters were embedded in the heating
chamber. The maximum output of each heater was 500W with AC 100V power supply. The input voltage of heaters
was adjusted by a slide regulator to change the temperature of the airflow. The geometry of the inflow pipe is shown in
Figure 4. The internal diameter of the pipe is 56.5mm and the centrally mounted nozzle holder has an outer diameter of
13.8mm. For generating the annular swirling airflow, a swirler is mounted 150mm above the pipe exit which consists of
four swirl vanes. The inclination of the swirl vanes with respect to the vertical axis is 60°. A Delavan type B solid cone
nozzle was used with the injection pressure of 0.8MPa, the flow rate of 5.3×10-7m3/sec and the working fluid of water.
The flow conditions for the non-heated and heated case are shown in table 1. The velocity of the airflow was measured
by a laser-Doppler anemometry. For comparing non-heated and heated condition the mean air velocity was kept almost
constant. The temperature was measured by a thermo-couple. Figure 5 shows the temperature distribution within the
measurement section at various cross-sections downstream of the pipe exit for the heated case. These measurements
were of course performed without the spray. The mean air inlet temperature for the heated case was about 373K. Due to
the mixing of the heated swirling jet with the surrounding air the temperature rapidly decays along the measurement
section.
2
Fig. 3. Schematics of experimental set-up and interferometric laser imaging technique
56.5
Table 1. Flow conditions
13.8
10.0 [mm]
non-heated
heated
u gas
1.2m/s
1.3m/s
Tgas
298K
373K
m gas
330g/s
280g/s
Re gas
42000
(obtain with D = 56.5mm)
45000
Fig. 4. Schematic drawing of inlet pipe with dimensions
3
400
380
360
340
320
300
0
5
10
15
20
25
30
35
zz=10mm
zz=20
zz=30
zz=40
zz=50
zz=60
zz=70
zz=80
zz=90
zz=100
Fig. 5. Temperature profiles along the measurement for the heated case without droplets
3. MEASUREMENT TECHNIQUE
When a spherical droplet is illuminated by laser light, the intensity of the reflected and refracted light from the droplet
are stronger than that of higher order refractions in the forward-scatter region between about 30 to 80deg. On the focal
image plane, two spots are observed as glare points (Van de Hulst and Wang 1991). Although the distance between the
glare points gives the particle size, it is difficult to evaluate the size thereby because of the lack of spatial resolution of
conventional receiving equipment. On a non-focal plane, the two rays interfere with each other and a parallel
interferogram is observed. ILIDS measures the diameter of a spherical transparent particle on the basis of the interfringe separation or the number of fringes within the interferogram. Girasole et al (2000) calculated the adequate
defocus distance and concluded that a sufficient defocusing distance is required for the far-field condition of the
receiving optics. Van de Hulst (1957) reported that a reasonable agreement between the geometric analysis and the full
Lorenz-Mie theory was obtained for the size parameter πd/λ > 20 for the condition that the refractive index of the
droplets differed significantly from its surrounding and that rays close to grazing incidence and those close to the
rainbow angles were not involved. For the present optical arrangement of λ = 532nm, the lower limit of the measured
droplet diameter is 2µm resulting from the geometric optical analysis.
The angular inter-fringe spacing is simply proportional to the droplet diameter and independent of the absolute light
intensity (Hesselbacher et al 1991, Toth et al 1991). It is easily derived by noting the phase difference between the
reflection and refraction from a single droplet. The relation between particle diameter d and the number of fringes N is
given by the following equation based on geometric optical analysis.
d=
2λN
α
1
m sin
θ
cos +
2
2
θ
2
m + 1 − 2m cos
(1)
θ
2
where λ is the wavelength of the laser light source and m is the relative refractive index of the liquid droplet. θ and α
are scattering and collecting angle, respectively. The fringe number N is equivalent to α divided by the angular interfringe spacing.
Figure 6 shows the dependence of the measured droplet diameter on the refractive index, resulting from Eq. 1 for a
scattering angle of 73deg. The calculated diameter, d, was normalized by the reference diameter, dref, of a water droplet
in an atmospheric temperature. The result shows that 1% increase or decrease of the relative refractive results in a
measurement error of less than 0.06% in diameter.
4
1.010
1.005
Relative refractive index 1.3100-1.3600
Scattering angle
73 deg
1.000
Water droplet in air
at 300K
0.995
0.990
1.3100 1.3200 1.3300 1.3400 1.3500 1.3600
m : Relative refractive index
Fig. 6. Refractive index dependency of a measured diameter.
A conventional interferometric laser imaging technique has the difficulty in discriminating the images of particles due
to the overlapping of the circular interferograms in high particle concentration regions. An interferential signal within
the fringe overlapping region is not a simple summation of a sinusoid and therefore the image processing of the
overlapped interferogram becomes complicated or even impossible.
Figure 7 illustrates the fundamental optical arrangement of the advanced interferometric laser imaging technique
(Maeda et al. 2000, 2002, Kawaguchi et al. 2002). A pair of cylindrical lenses was placed between the imaging plane
and the objective lens in order to project the horizontal out-of-focus images on a vertically focused plane. The
cylindrical lens can be moved along the optical axis of the receiving optics that enables to adjust the degree of
horizontal defocusing. By using the squeezing optical system, such confusing image overlapping as in the conventional
ILIDS techniques had been drastically reduced.
Laser sheet
Droplet
Cylindrical lens
Collecting lens
Rectangular aperture
Imaging plane
Fringe image
Fig. 7. Optical arrangement of the advanced interferometric laser imaging technique.
After the sequential acquisition of the images with linear interferograms, a fully automated image processing of the
interferograms was carried out by an original code on a personal computer. The software identifies the individual fringe
images and determines their location within the image. The interferogram can be detected by scanning the captured
image horizontally that gives a similar signal as the Doppler burst signal for the LDV technique. The concept of the
signal processing procedure for the evaluation of fringe spacing is the same as that of FFT based LDV/PDA processing
techniques by which the accurate frequency is calculated with the adjusted Gaussian fitting method for the discrete
Fourier power spectrum (Kobashi et al. 1990). The interpolation technique is effective in the reduction of bias errors to
less than 0.2% for the fundamental frequency. The resultant resolution of the measured fringe count, which is directly
proportional to the diameter, becomes much higher than the simple peak determination of the power spectrum. The
accurate diameter determination by the interpolation technique contributes to the particle tracking and velocity
calculation since the precise diameter information, which conventional particle tracking techniques does not survey,
enables us to find the corresponding particles between the image pairs. For the determination of the droplet velocities a
particle tracking technique was employed (Maeda et al. 2002). For this purpose the centroids of the squeezed droplet
images were obtained for two subsequent images (Figure 8).
5
Interrogation
Interrogation window
Reference
window
Reference
window
(Ǎx, Ǎy)
Fig. 8. Particle tracking technique for the determination of the droplet velocities
The measurement equipment consisted of a pulsed laser, transmitting and receiving optics, CCD camera and personal
computer with frame grabber. The light source was a dual pulsed Nd:YAG laser with 532nm wavelength, the
maximum output power was 120mJ/pulse, the repetition frequency was up to 15Hz, the time interval between laser
pulses was set to 6µs. The thickness of the laser sheet was 0.5mm within the test section. Circularly polarized light was
used for a better discrimination between interferogram and background. The imaging device was a digital CCD camera
with 1008×1018 pixels, each pixel has a 10bit grayscale level. The size of the measuring area was set to 10mm×10mm,
which depends on the magnification ratio of the receiving optics. The distance from the objective lens to the test section
was 180mm and the collecting angle was 5deg. The scattering angle was set to 73deg to receive high visibility
interference by equalizing the intensity of reflection and refraction.
4. RESULTS AND DISCUSSION
A Snapshot of the steady spray in a non-heated swirling flow is shown in Figure 9. Measurements of the droplet size
and velocity were conducted at 15 locations within the spray where the axial locations are z =25,45,75,105mm and the
radial locations are r = 0, 10, 20, 30mm (at z=25mm, r=30mm, there are almost no droplet). At each measuring location
1430 pairs of the images were taken to obtain the information of droplets that exist in a 10mm×10mm measuring area.
9mm
Fig. 9. Snapshot of a steady spray in a swirling flow
6
The probability density functions of the droplet diameter for the non-heated case are shown in Figure 10. Along the
center of the spray, the number of the larger droplets increases compared to the smaller ones. Thereby, a bimodal
droplet size distribution develops. This is a result of the interaction of the spray with the central recirculation region,
causing the smaller droplets to be radially transported outward since they are able to respond to the airflow. The larger
droplets penetrate the recirculation region to a large extent (Sommerfeld and Qiu 1993). At the same axial location, the
number of smaller droplets increases at the edge of the spray. This is a result of the fact that the smaller droplets follow
the swirling flow and are carried away from the central region toward the edge of the spray.
Figure 11 shows the correlation maps between the droplet diameter and axial velocity for the non-heated case. Near the
nozzle the droplets are fast up to about 10m/s. Along the spray core, smaller droplets are decelerated rather fast,
whereas the inertia of the larger droplets is associated with a slower decrease of their axial velocity. Far downstream of
the spray nozzle and at the edge of the spray, there exists almost no correlation between the axial droplet velocity and
their size, indicating that all droplets move at about the same velocity. The negative droplet velocities found within the
spray are the result of the droplet interaction with the central recirculation region. A higher probability for such
negative velocities is found in a region 25-45mm downstream of the nozzle exit and between r=10-20mm, of course the
smaller droplets have higher negative velocities. This observation is in accordance with the droplet trajectory
calculations introduced by Sommerfeld and Qiu (1993). If small droplets enter centrally the recirculation region, they
are decelerated and transported upward torwards the nozzle exit while moving radially outward due to the centrifuging
effect. Hence, also the number of the droplets near the center of the spray decreases along the spray.
The size distributions an the centre line of the spray comparing the non-heated and heated case are shown in Figure 12.
Droplet evaporation in the heated case yields a faster decrease of the mean droplet size along the spray than for the
non-heated case. Also for the heated case a bimodal droplet size distribution develops within the recirculation zone.
Figure 14 shows profiles of the Sauter mean diameter and the arithmetic mean diameter of droplets in the radial and
axial direction, respectively. The droplet transport processes in a swirling flow described above cause a decrease of the
droplet diameters from the centre line towards the edge of the spray (Figure 14 left). As expected, the droplet mean
diameters are smaller for the heated case. Along the spray centre line the arithmetic mean droplet diameter increases
due to the radial transport of the smaller droplets (Figure 14 right). The Sauter mean diameter first decreases, reaches a
minimum and then increases again. This indicates that the droplet size distribution initially becomes more narrow and
then broadens again. In the heated case the minimum of the SMD is located further downstream of the spray nozzle exit.
Also the mean diameters are smaller for the heated case due to droplet evaporation.
Figure 13 compares the correlation maps between the droplet diameter and axial velocity for the non-heated and heated
case. In the heated case the droplets have a somewhat higher velocity than in the non-heated case and also the
correlation between size and velocity is strange. This might be associated with a slightly higher liquid velocity at the
nozzle exit, since the water may be heated when flowing through the nozzle holder.
7
Fig. 1 .
robability density f nctions of the droplet diameter for the non-heated
Fig. 11. Correlation maps between the axial velocity component, and the droplet size for the non-heated case
8
r=0
r=0
Fig. 12. Droplet size distributions comparing
The non-heated and the heated cases
r=0mm
60
SMD
11111
50 (non-heated)
z=75mm
60
50
SMD (non-heated)
11111
SMD (heated)
22222
AMD (non-heated)
33333
44444
AMD (heated)
SMD (heated)
22222
40
33333
AMD (non-heated)
30
44444
AMD (heated)
d(µm)
d(µm)
Fig. 13. Correlation maps between the diameter and
the axial velocity
40
30
20
20
0
10
20
r(mm)
30
25
45
75
z(mm)
105
Fig. 14. Sauter and Arithmetic mean diameters of droplets (i.e. SMD and AMD) in the
radial direction at z=75mm (left) and along the centre line of the spray (right)
5. SUMMARY
The behaviour of a water spray centrally injected into a swirling annular jet has been studied by applying
interferometric laser imaging technique. Two flow conditions were compared, namely a non-heated and a heated
airflow issuing into quiescent air. The results demonstrate that the interaction of the spray with the swirling free jet
flow and the established recirculation zone results in bimodal droplet size distributions for both the non-heated and
heated case. As expected, droplet evaporation in the heated case yields a faster decrease of the arithmetic mean droplet
size along the spray than for the non-heated case. The distribution of the Sauter diameter along the spray shows a
distinct minimum for both cases. This implies that the width of the droplet size distribution is first decreasing. Further
studies will be performed for different swile numbers as sell as air injection temperatures.
9
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